Continuous Medium Model for Fractal Media

By Vasily E. Tarasov. 2005

238 citations recorded by the source corpus.

We consider the description of the fractal media that uses the fractional integrals. We derive the fractional generalizations of the equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with non-integer mass dimensions. The fractional equation of continuity is considered.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/87ec53c69f89f47c0487dde61ae1023bb56ed65d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

1. Martin Ostoja-Starzewski
2. Jun Li
3. Vasily E. Tarasov

In Numerical Analysis

1. Martin Ostoja-Starzewski
2. Jun Li

Citations in the corpus

• Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[216] V.”
• Fractal solids, product measures and fractional wave equations (2009, methodology): “Now, following Tarasov (2005a), the fractional integral is employed to represent mass in a three-dimensional region W m(W ) = ∫ W ρ(r) dVD = ∫ W ρ(r)c3(D, r) dV3.”
• Systems of Navier-Stokes equations on Cantor sets (2013, unknown): “The results are different from [36–38] because of the fractional operators.”